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In a vibrating system, a particular vibrational mode can be described as a harmonic
oscillator with some mass and stiffness. Given some measure of vibrational
amplitude, there exists a unique choice of mass and stiffness that yields the
correct values for both frequency and energy; these are the effective mass and
effective stiffness.

An object behaves elastically if it returns to its original shape after a force is
applied and then removed. (If an applied force causes a permanent deformation, the
behavior is termed plastic.) In an elastic system, the internal potential
energy is a function of shape alone, independent of past forces and deformations.

The location of an electron is not fixed, but is instead described by a probability
density function. The sum of the probability densities of all the electrons in a
region is the electron density in that region.

A measure of the tendency of an atom (or moiety) to withdraw electrons from
structures to which it is bonded. In most circumstances, for example, sodium tends
to donate electron density (it has a low electronegativity) and fluorine tends to
withdraw electron density (it has a high electronegativity).

A transformation is termed endothermic if it absorbs energy in the form of heat. A
typical endothermic reaction increases both
entropy and molecular potential energy (and is thus analogous to
a gas expanding while absorbing heat and compressing a spring).

A conserved quantity that can be interconverted among many forms, including
kinetic energy, potential energy, and electromagnetic
energy. Sometimes defined as "the capacity to do work,'' but in an environment at a uniform nonzero
temperature, thermal energy does not provide this
capacity. (Note, however, that all energy has mass, and thus can be used to do work
by virtue of its gravitational potential energy; this caveat, however, is of no
practical significance unless a really deep gravity well is available.)
See free energy.

The enthalpy of a system is its actual energy
(termed the internal energy) plus the product of its volume and the
external pressure. Though sometimes termed "heat content,'' the enthalpy in fact
includes energy not contained in the system. Enthalpy proves convenient
for describing processes in gases and liquids in laboratory environments, if one
does not wish to account explicitly for energy stored in the atmosphere by work
done when a system expands. It is of little use, however, in describing processes
in nanomechanical systems, where work
can take many forms: internal energy is then more convenient. Enthalpy is to energy
what the Gibbs free energy is
to the Helmholtz free
energy.

A measure of uncertainty regarding the state of a system: for example, a gas
molecule at an unknown location in a large volume has a higher entropy than one
known to be confined to a smaller volume. Free energy can be extracted in converting a
low-entropy state to a high-entropy state: the (time-average) pressure exerted by a
gas molecule can do useful work as a small volume is expanded to a larger volume.
In the classical configuration
space picture, any molecular system can be viewed as a single-particle gas in a
high-dimensional space. In the quantum mechanical picture, entropy is described as
a function of the probabilities of occupancy of different members of a set of
alternative quantum states. Increased information regarding the state of a system
reduces its entropy and thereby increases its free energy, as shown by the
resulting ability to extract more work from it.
An illustrative contradiction in the simple textbook view of entropy as a local
property of a material (defining an entropy per mole, and so forth) can be shown as
follows: The third law of thermodynamics states that a perfect crystal at absolute
zero has zero entropy*; this is true regardless of
its size. A piece of disordered material, such as a glass, has some finite entropy
G0 > 0 at absolute zero. In the
local-property view, N pieces of glass, even (or especially) if all are
atomically identical, must have an entropy of NG0. If these
N pieces of glass are arranged in a regular three-dimensional lattice,
however, the resulting structure constitutes a perfect crystal (with a large unit
cell); at absolute zero, the third law states that this crystal has zero entropy,
not NG0. To understand the informational perspective on
entropy, it is a useful exercise to consider (1) what the actual entropy of such
crystal is as a function of N, with and without information describing the
structure of the unit cell, (2) how the third law can be phrased more precisely,
and (3) what this more precise statement implies for the entropy of well-defined
aperiodic structures. Note that any one unit cell in the crystal can be regarded as
a description of all the rest.

A system is said to be at equilibrium (with respect to some set of feasible
transformations) if it has minimal free
energy. A system containing objects at different temperatures is in disequilibrium, because heat
flow can reduce the free energy. Springs have equilibrium lengths, reactants and
products in solution have equilibrium concentrations, thermally excited systems
have equilibrium probabilities of occupying various states, and so forth.

Characterized by precise molecular order, like that of a perfect crystal, the
interior of a protein molecule, or a
machine-phase system; contrasted to the disorder of bulk materials, solution
environments, or biological structures on a cellular scale. Borderline cases can be
identified, but perfection is not necessary. As a crystal with sparse defects is
best described as a crystal (rather than as amorphous), so a eutactic structure
with sparse defects is best described as (imperfectly) eutactic, rather than as
disordered.

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* Some textbooks state a slightly weaker form: a reaction that converts perfect
crystals at absolute zero into other perfect crystals at absolute zero results in
no change in entropy. This is essentially equivalent.